Radiation View Factor Reciprocity Check
Radiation View Factor Reciprocity Check
Radiation heat exchange between two surfaces depends on the view factor, the fraction of radiation leaving one surface that directly strikes the other, and these factors are usually looked up from charts or computed for specific geometries — but they are never independent of each other. The reciprocity relation, F12·A1 = F21·A2, is both a useful shortcut (once F12 is known, F21 follows immediately without a second lookup) and a mandatory consistency check: any pair of view factors that violates reciprocity indicates an error somewhere in the geometry or chart reading, so engineers routinely use this relation to catch mistakes before running a full radiation network calculation.
The reciprocity relation is F12·A1 = F21·A2, which rearranges to F21 = F12·A1/A2. where F12 is the view factor from surface 1 to surface 2, A1 and A2 are the surface areas, and F21 is the view factor from surface 2 to surface 1.
Inputs
A_1r := 2 m^2=2 m^2
F_12 := 0.35=0.35
A_2r := 3.5 m^2=3.5 m^2
Applying the reciprocity relation converts the known view factor and areas into the reverse-direction view factor, without needing to separately look up or compute F21 from geometry.
F_21 := F_12·A_1r/A_2r=0.2
Results
The resulting F21 = 0.2 is physically sensible: since surface 2 is larger than surface 1, radiation leaving surface 2 is spread over more directions, so a smaller fraction of it happens to strike surface 1, and F21 correctly comes out smaller than F12. Both view factors must also individually lie between 0 and 1, and in an enclosure the sum of all view factors leaving a surface (including to itself, if it is concave) must equal 1 — checking both bounds is standard practice before trusting a view factor value in a radiation network calculation. If reciprocity or these bounds fail, the geometry or the source chart was misread.
Assumptions & limitations
- Diffuse, gray surfaces assumed (view factors defined for diffuse radiation exchange).
- No participating medium (transparent, non-absorbing intervening gas).
- F12 assumed already correctly determined from chart or geometric calculation.
- Surfaces assumed to have uniform radiosity across their area.